There's only so much you can assume, but it's likely that the motors are in the 13000-18000 RPM range stock. You could pick up a set of the $3 23000 RPM Nichibo motors listed in this motor sticky thread and swap them in. You may or may not be able to use the stock pinions -- I was able to do so with Power Wheels pinions (they normally press-on to a swaged shaft on the motor -- so had to swage the smooth new motor shafts as much as I could and add a little red loctite, but haven't had any problems on the four I've swapped).

In theory this would likely give you 40-60% more speed, which may not hit your 10km/hr goal. Be forewarned that the stall current is likely a bit higher, you do still run some risk of damaging the circuit board (well-designed ones will have current-limiting built in and it won't cause any problems).

Can you take a measurement of the full case length of the motor? Those generally come in two sizes -- I expect yours will be 50mm long based on the label:

50mm long - "540" class - popular in RC cars57mm long - "550" class - used in a lot of the ride-on toys

Normally I'd recommend buying the longer ones as replacements if you can find them as you'll get more torque per amp, which you'll want if you are getting a motor that spins faster (which means less winding = more RPM but lower torque per amp). However, most of the 550s come with torque sleeves (and extra metal sleeve on the outside) which isn't going to work with the factory mounting. One option-that doesn't have a flux ring (but it's only give you a 33% speed boost): https://www.conrad.de/de/universal-brushed-elektromotor-motraxx-x-drive-550-1-10500-umin-244465.html

As far as direct fit motors, you're going to want a fairly high-turn motor. Looking at the Conrad site, you can see that the turns vs. RPM look about like this for this size motor in the Absima line -- I think these are mostly 7.2V motors:

If you got one of these you'd be running it at a higher voltage than nominal, and it's hard to know how long they'd last; the windings. In that case I would recommend getting the 50turn one; if it's 8300 RPM @ 7.2V, then it will be around 13500 RPM @ 12V.

Regardless, you're going to need to measure the gear diameter and figure out if it's mod 1.0 or mod0.8. Then you'll buy a gear that fits on a 1/8" / 3.2mm shaft (not a 2mm one).

If you're going to be limited to the 540 can size, then those look like they're probably going to be a decent fit for the application. I'm used to seeing vented (with integrated fan) motors on the ride-on toys and I'd be worried about overheating these. You do have 4 (vs. the standard 2wd ones I use), so it will spread the load out some. Do your current motors have a built-in fan, like this one:

(you can see the small plastic fan on the 2nd image). Also, it's hard to tell from the gearbox photo, but are the front holes on the motor open (and thus can breathe), or is it all closed up. If they're blocked then it won't matter anyway unless you want to start doing a lot of gearbox modification. The fan sucks air through the front holes so if they're blocked it won't be effective.

There is a place for 550's if they are longer.I'll purchase 2 of them and swap the rear ones.I'll disable the front ones because those two 550 are rated at 105 watt each.Mines are rated at 35-45 watt, so together it's 180 watt. Not sure if that ESC can handle 420 watt load with four 550, I can't find any info about that.Or it's ok and I should go with 4 of them?

Most of the ESCs should have current limiting built in and really shouldn't have a problem with any motors you use. These controllers appear to be listed for about $17 on ebay, and like most of the cheaper scooter drivers, will likely have a very low current limit, in the 25-40A range. Moving from 8000 RPM motors to 18000 RPM motors (at equal voltage) means you'll likely lose 50% of your torque. It's going to be a bit slower off the line, although it should still be ok as long as you're not trying to go up steeper hills. Running two motors vs. 4 isn't going to make much difference in the current-limited region -- it will just distribute the load between the available motors; you'll lose the traction advantage of 4WD. Stall current for 2x of those 18000 RPM ones is likely in the 60-80A range (each) -- but 2x of those will likely not be substantially more load than 4x of the current ones.

It's going to require quite a bit of work to install other controllers and keep the remote functional. Personally, I'd try the faster motors with the stock controller, but I also have an oscilloscope and lots of components lying around -- but having the option to get a replacement for $25 or $30 shipped seems like a good fallback if the board does fail.